1. ## roots of the quadratic equation

Given the root of the quadratic equation of $\displaystyle 4ax^2+bx+8=0$ are equal.Express $\displaystyle a$ in terms of $\displaystyle b$

2. Originally Posted by lindros
Given the root of the quadratic equation of $\displaystyle 4ax^2+bx+8=0$ are equal.Express $\displaystyle a$ in terms of $\displaystyle b$
The question tells you that $\displaystyle 4ax^2+bx+8=0$ is a square (the square of a linear term) , now try it and if you have further problems post what you have tried or what you do not understand

CB

3. You know the quadratic formula, don't you: $\displaystyle x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}$

The two roots will be equal if and only if the square root is 0.

Another way to do this is to write the equation as $\displaystyle 4ax^2+ bx+ 8= 4a(x- x_0)(x- x_0)$. Multiply the right side and set corresponding coefficients equal.

4. Originally Posted by lindros
Given the root of the quadratic equation of $\displaystyle 4ax^2+bx+8=0$ are equal.Express $\displaystyle a$ in terms of $\displaystyle b$

Use the following: if $\displaystyle \alpha\,,\,\beta$ are the roots of $\displaystyle ax^2+bx+c=0\,,\,\,a\neq 0$ , then $\displaystyle \alpha\beta=\frac{c}{a}\,,\,\,\alpha+\beta=-\frac{b}{a}$ .

You can also google "Viete's formulae"

Tonio